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Towards the Proof of AGT Relations with the Help of the Generalized Jack Polynomials

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Original proofs of the AGT relations with the help of the Hubbard–Stratanovich duality of the modified Dotsenko–Fateev matrix model did not work for β ≠ 1, because Nekrasov functions were not properly reproduced by Selberg–Kadell integrals of Jack polynomials. We demonstrate that if the generalized Jack polynomials, depending on the N-ples of Young diagrams from the very beginning, are used instead of the N-linear combinations of ordinary Jacks, this resolves the problem. Such polynomials naturally arise as special elements in the equivariant cohomologies of the GL(N)-instanton moduli spaces, and this also establishes connection to alternative ABBFLT approach to the AGT relations, studying the action of chiral algebras on the instanton moduli spaces. In this paper, we describe a complete proof of AGT in the simple case of GL(2) (N = 2) Yang–Mills theory, i.e., the 4-point spherical conformal block of the Virasoro algebra.

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  1. ITEP, Moscow, Russia

    Alexei Morozov

  2. Department of Mathematics, Columbia University, New York, USA

    Andrey Smirnov

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  1. Alexei Morozov
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  2. Andrey Smirnov
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Morozov, A., Smirnov, A. Towards the Proof of AGT Relations with the Help of the Generalized Jack Polynomials. Lett Math Phys 104, 585–612 (2014). https://doi.org/10.1007/s11005-014-0681-6

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